calculate-0-t-2-e-t-1-dt-interms-of-3- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 53783 by maxmathsup by imad last updated on 25/Jan/19 calculate∫0∞t2et−1dtintermsofξ(3) Answered by Smail last updated on 26/Jan/19 A∫0∞t2et−1dt=∫0∞t2e−t1−e−tdt=∫0∞t2e−t∑∞n=0e−ntdt=∑∞n=0∫0∞t2e−(n+1)tdtbypartsu=t2⇒u′=2tv′=e−(n+1)t⇒v=−1n+1e−(n+1)tA=∑∞n=02n+1∫0∞te−(n+1)tdtwith([t2e−(n+1)t]0∞=0)bypartsA=∑∞n=02(n+1)2∫0∞e−(n+1)tdt=∑∞n=02(n+1)3[e−(n+1)t]0∞=2∑∞n=01(n+1)3=2∑∞n=11n3=2ξ(3) Commented by maxmathsup by imad last updated on 26/Jan/19 thankyousir Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: calculate-0-1-t-2-1-t-3-dt-Next Next post: n-o-oo-1-n-x-2n-1-4n-2-1- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.